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A soliton hierarchy derived from a fourth-order matrix spectral problem possessing four fields

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  • Ma, Wen-Xiu

Abstract

This paper is dedicated to the construction of integrable commuting flows starting from a fourth-order matrix spectral problem involving four fields, which is derived from a specialized matrix Lie algebra over the real domain. This work includes the development of an explicit bi-Hamiltonian formulation and a hereditary recursion structure, which confirms the hierarchy’s integrability in the Liouville sense. Furthermore, we examine two second-order and third-order integrable models, along with their reduced, uncombined forms.

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  • Ma, Wen-Xiu, 2025. "A soliton hierarchy derived from a fourth-order matrix spectral problem possessing four fields," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:chsofr:v:195:y:2025:i:c:s0960077925003224
    DOI: 10.1016/j.chaos.2025.116309
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    References listed on IDEAS

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    1. Xia, Tiecheng & Yu, Fajun & Zhang, Yi, 2004. "The multi-component coupled Burgers hierarchy of soliton equations and its multi-component integrable couplings system with two arbitrary functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 238-246.
    2. Yang, Sheng-Xiong & Wang, Yu-Feng & Zhang, Xi, 2023. "Conservation laws, Darboux transformation and localized waves for the N-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Ye, Rusuo & Zhang, Yi, 2023. "A vectorial Darboux transformation for the Fokas–Lenells system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
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